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Complete bandgaps in two-dimensional phononic crystal slabs with resonators
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10.1063/1.4816273
/content/aip/journal/jap/114/4/10.1063/1.4816273
http://aip.metastore.ingenta.com/content/aip/journal/jap/114/4/10.1063/1.4816273

Figures

Image of FIG. 1.
FIG. 1.

Unit cells and finite element models of (a) open and (b) covered PC slabs and the associated geometry parameters.

Image of FIG. 2.
FIG. 2.

Cross-section of (a) the open or (b) covered PC slab parallel and (c) perpendicular with the thickness direction.

Image of FIG. 3.
FIG. 3.

Cross-sections of the unit cells in the median plane and their corresponding irreducible Brillouin zone.

Image of FIG. 4.
FIG. 4.

Band structures of various open PC slabs: (a) Slab “O1”; (b) Slab “O2(a)”; (c) Slab “O2(o)”; (d) Slab “O3”; (e) Slab “O4”. The geometry parameters are / = 0.9, / = 0.8, / = 0.05 and / = 1. For comparison, the band structure for a PC slab with cuboid holes (/ = 0.9 and / = 1) is shown in panel (f).

Image of FIG. 5.
FIG. 5.

cross-section of the eigen modes at the bandgap edges marked in Fig. 3

Image of FIG. 6.
FIG. 6.

Effects of the thickness of slab “O2(a)” on the bandgaps (/ = 0.8, / = 0.05). The thick solid line shows the predicted result obtained by the equivalent model. The dashed and dashed-dotted lines represent the numerical results of the lower and upper edges of the bandgap, respectively.

Image of FIG. 7.
FIG. 7.

Effects of the size of the lumps / (with / = 0.05, / = 1) (a) or the connectors / (with / = 0.8, / = 1) (b) on the bandgaps of slab “O2(a).”

Image of FIG. 8.
FIG. 8.

Band structures for (a) slab “C1-0” and (b) covered PC slab with cubic holes. The geometrical parameters are / = 0.9, / = 0.8, / = 0.05 and / = 1.

Image of FIG. 9.
FIG. 9.

Eigen modes in plane at the bandgap edges of slab “C1-0” as shown in Fig. 7(a) .

Image of FIG. 10.
FIG. 10.

Band structures for various covered PC slabs (a) slab “C2(a)-0”; (b) slab “C2(o)-0”; (c) slab “C2(a)-1”; (d) slab “C2(a)-2”; (e) slab “C4-1”; (f) slab “C4-2”. The geometrical parameters are / = 0.9, / = 0.8, / = 0.05, and / = 1.

Image of FIG. 11.
FIG. 11.

Eigen modes in plane [(a)–(c)] and plane [(d)–(j)] at the bandgap edges for covered PC slabs shown in Fig. 10 .

Image of FIG. 12.
FIG. 12.

(a) Effects of the cover thickness on the bandgaps for slab “C2(a)-2” (with / = 0.8, / = 0.05, / = 0.9, and / = 1) (b) cross-section of the eigen mode at the lower edge of the bandgap for slab ‘C2(a)-2’ with .

Image of FIG. 13.
FIG. 13.

Effects of the size of the connectors / (with / = 0.8,  = 0.05, / = 0.9, and / = 1) (a) or (with / = 0.8, / = 0.05, / = 0.9, and / = 1) (b) on the bandgaps for slab “C2(a)-2.”

Image of FIG. 14.
FIG. 14.

Effects of the size of the lump / ( / = 0.8, / = 0.05, / = 0.9, and / = 1) (a) or / (/ = 0.8, / = 0.05, / = 0.9, and / = 1) (b) on the bandgaps for slab “C2(a)-2.”

Tables

Generic image for table
Table I.

Open PC slab with different connector distributions for / = 0.9 and / = 1.

Generic image for table
Table II.

Covered PC slab with different connector distributions for / = 0.9 and / = 1.

Generic image for table
Table III.

Calculation of the effective stiffness of the proposed spring-mass/pendulum models for the lower edge modes of the open PC slab.

Generic image for table
Table IV.

Calculation of the effective stiffness of the proposed spring-mass/pendulum models for the lower edge modes of the covered PC slab.

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/content/aip/journal/jap/114/4/10.1063/1.4816273
2013-07-24
2014-04-19
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Complete bandgaps in two-dimensional phononic crystal slabs with resonators
http://aip.metastore.ingenta.com/content/aip/journal/jap/114/4/10.1063/1.4816273
10.1063/1.4816273
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